A group decision making with probability linguistic preference relations based on nonlinear optimization model and fuzzy
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A group decision making with probability linguistic preference relations based on nonlinear optimization model and fuzzy cooperative games Pei Liang1 · Junhua Hu1 · Bo Li1 · Yongmei Liu1 · Xiaohong Chen1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The aim of the paper is to solve the group decision making problems which contain inconsistent probabilistic linguistic preference relations (PLPRs) and unknown expert weights. When the PLPRs are inconsistent, there are contradictories in the preference relations expressed by the experts. The evaluation value with contradictory information will bring out an incorrect consequence in decision making. Hence, this paper develops a novel consistency measure method to gauge the consistency level of PLPRs. Moreover, a nonlinear optimization model is newly constructed to optimize the inconsistent PLPRs. The proposed methods overcome the limitations in the existing methods and ameliorate the interpretation and complexities of inconsistency PLPRs revise strategies. Additionally, a weighting method using fuzzy cooperative games with PLPRs is put forward to derive the weight vector of experts. It helps to balance the deviations between the individual PLPRs and the group PLRP. At last, a numerical example illustration for physician selection is put forward to demonstrate the effectiveness of the proposed model and its practical applicability. The comparative analysis gives deep insights into the rationality of the proposed model. Keywords PLPR · PLTS · PLE · Consistency · Cooperative game
1 Introduction Group decision making (GDM) is the most common approach used in complex decision making process. In general, several decision makers (DMs), usually the experts in their fields, are invited to externalize their preferences for the alternatives to arrive at a final decision by aggregating those preferences. In practice, the preferences for alternatives given by the individuals are the perceptions gained from an adequate semantic
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Junhua Hu [email protected] School of Business, Central South University, Changsha 410083, China
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P. Liang et al.
scale, and the pairwise comparison values are expressed as qualitative description rather than numerical values (Zadeh 1974). For example, the decision makers choose ‘good’, ‘slightly bad’, and ‘very good’ to express their preferences for the alternatives. Those linguistic terms are inherently uncertain and can’t be directly used for quantitative calculation. To solve the problem, many conceptions are proposed during the evaluation process. Those conceptions include 2-tuple fuzzy linguistic preference relations (2TFLPRs) (Herrera and Martinez 2000), hesitant fuzzy linguistic terms (HFLTs) (Rodriguez et al. 2012) and hesitant fuzzy linguistic preference relations (HFLPRs) (Sun et al. 2018). These conceptions deliver the uncertainty and fuzziness in the linguistic terms. But there is limitation along with them. Let take HFLTs and HFLPRs as examples. Rodriguez et al. (2012) gave the definition of HFLTs
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